Abstract The integral transform method based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the generalized Weyl space-fractional operator. The solutions, representing ...

Analytical solutions of integral equations, either do not exist or are hard to find. Due to this, many numerical methods have been developed for finding the solutions of integral equations. The use of wavelets has come to prominence during the last two decades. Wavelets can be used as analytical tools for signal processing, numerical analysis and mathematical modeling. The early works concernin...

The differential transform method and Herrera’s complex integral method are shown to be related through the Taylor-Cauchy transform, which appears as a genuine fore-runner of both methods. A short discussion of this result is provided. Mathematics Subject Classification: 34A05, 34A25, 34A30, 34A34, 35C10

The integral of a function defined on the half-plane along the semi-circles centered on the boundary of the half-plane is known as the circular averages transform. Circular averages transform arises in many tomographic image reconstruction problems. In particular, in synthetic aperture radar (SAR) when the transmitting and receiving antennas are colocated, the received signal is modeled as the ...

this paper presents the application of radial basis neural networks to the development of a novel method for the condition monitoring and fault diagnosis of synchronous generators. in the proposed scheme, flux linkage analysis is used to reach a decision. probabilistic neural network (pnn) and discrete wavelet transform (dwt) are used in design of fault diagnosis system. pnn as main part of thi...

A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the ...

Abstract—In this paper, we consider the resistances and inductances extraction from finite conducting metals. To remedy the weakness of volume integral equation, we extend the usage of a surface integral equation method from analyzing finite conducting rectangular wire strip to analyzing arbitrarily shaped geometry. Moreover the multilevel Green function method (MLGFIM) with a complexity of O(N...

A new method is presented for shape sensitivity analysis of a crack in a homogeneous, isotropic, and linear-elastic body subject to mode-I loading conditions. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the pro...

Using finite element methods, we need to answer these questions: • What is the appropriate functional space V for the solution? • What is the appropriate weak or variational form of a differential equation? • What kind of basis functions or finite element spaces should we choose? • How accurate is the finite element solution? We briefly address these questions in this Chapter. Recalling that fi...